A study showed that vitamin A oil reduces pain levels in patients with Lyme disease. During each session, the oil was injected into the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session. Another study is being designed to examine whether vitamin A oil also reduces pain in patients suffering from pinched nerves in the cervical region of the back. Two hundred patients aged 20-40 years are subjects in the new study. Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (5 points) Part B: If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20-40, would you change the study design? If so, how would you modify your design? If not, why not? (5 points) Part C: Suppose the data in the following table was collected at the end of the study you described in part A. Vitamin A Oil Placebo Reported Pain Reduction 37 21 Total Treated 100 100 Construct 90% confidence intervals for the proportion of pain reduction for each treatment group. Show all work. (5 points) Part D: What can you conclude about the use of vitamin A oil for patients with pinched nerves in the cervical region of the back? (5 points)